Debt and Cost of Capital





Kerry Back

Overview

  • Adding debt increases enterprise value because of the tax savings, up to a point.
  • Enterprise value is free cash flow discounted at the WACC.
  • Debt and interest do not affect free cash flow.
  • So adding debt must reduce the WACC.
  • The effect is through taxes, not just because debt is cheaper capital.

If there were no taxes …

  • WACC = % equity \(\times\) cost of equity + % debt \(\times\) cost of debt
  • Consider all equity firm that switches to part debt. Perpetuity model.
  • Example: equity value = enterprise value = $100, so expected free cash flow / cost of equity = $100.
  • Issue riskless debt paying $1 per year in perpetuity at risk-free rate of 5%.

  • Market value of debt is $1 / 0.05 = $20
  • Use $20 to repurchase shares. Firm is now $80 equity and $20 debt.
  • WACC is 0.8 \(\times\) new cost of equity + 0.2 \(\times\) 0.05.
  • Claim: WACC is equal to old cost of equity
    • This means cost of equity rises with leverage to offset use of cheaper debt capital.

  • Example: old cost of equity is 11%.
  • Claim: 0.8 \(\times\) new cost of equity + 0.2 \(\times\) 0.05 = 0.11.
  • This means new cost of equity is 12.5%.
  • Why?
    • All risk piled on $80 of equity instead of $100 means equity risk per dollar is 10/8 of what it used to be.
    • Risk premium should be 10/8 of what it used to be.
      • Old risk premium was 11% - 5% = 6%
      • New risk premium is (10/8) \(\times\) 6% = 7.5%
      • New cost of equity is 5% + 7.5% = 12.5%.

But there are taxes …